So is a longer story, but if you look here, if you setup the Flow to be Run only User, then they will use their own connection (per the description), but this doesn't work for all Flows. Not all flows can do this.
In other cases, you while technically you can share connections, you have to be careful. Sharing a connection doesn't relinquish the need for users to have licenses. It simply runs everything as the "connected/flow creator" so please watch that. If you were to for instance try to do that with Dataverse, that requires a license for everyone and instead you bypassed that, while in cases you can, its not a legic (against licensing eula).
In your case, did you setup Run only User?
If you shared the Flow, did you share the Agent and can you show some pictures of how you "shared" the connection, because that is not a guarantee that it won't prompt them because you also have to configure inside the Agent itself too.
Its a .. sometimes very convoluted issue.
Can you walk down the list and explain end to end your security settings from both within the Agent, Flow and Teams with pictures? please
If these suggestions help resolve your issue, Please consider Marking the answer as such and also maybe a like.
Thank you!
Sincerely, Michael Gernaey
